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Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.A deck of 52 cards is shuffledQuantity I: Two cards are picked at random, what is the probability of choosing first cards between numbers 5 to 9 (include 5 and 9) and second card being greater than or equal to queen but less than ace.Quantity II: A card is picked at random, what is the probability of it being either from 1-5 (include 1 and 5) number or greater than a queen. 1. Quantity I ≥ Quantity II2. Quantity I ≤ Quantity II3. Quantity I > Quantity II4. Quantity I = Quantity II5. Quantity I < Quantity II |
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Answer» Correct Answer - Option 5 : Quantity I < Quantity II Given: First card drawn = 5 to 9 Second card drawn = greater than or equal to queen but less than ace Two cards = either between 1-5 or greater than a queen Calculation: Quantity I : Probability of card being in between 5 to 9 = (5 × 4)/52 (∵ 5 -9 = 5 and 4 colors so 20) ⇒ Probability of card being in between 5 to 9 = 5/13 Probability of card being greater than or equal to queen but less than ace = (2 × 4)/51 ⇒ Probability of card being greater than or equal to queen but less than ace = 8/51 Required probability = (5/13) × (8/51) ⇒ required probability = 40/663 Quantity II : Probability of card being from 1-5 = 20/52 (∵ 5 to 1 = 5 cards so 20 cards in total) Probability of card being from 1-5 = 5/13 Probability of card greater than queen = (2 × 4)/52 (∵ only king and ace of all colors are greater than queen) ⇒ Probability of card greater than queen = 2/13 Required probability = (5/13) + (2/13) ⇒ required probability = 7/13 ∴ Quantity I < Quantity II |
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